Age of Universe/Earth

I was discussing religion/physics with a girl who is a strong Christian and although she was massively misinformed in almost every topic dealing with physics, she did bring up an interesting point that I had not heard before. She said that she read somewhere that there were conflicting views on dating techniques that produce different ages of materials. However I tried to explain that no dating technique produced an age of the earth even close to what she thought, less than 10,000 years of age (lol she thought that dinosaurs and humans lived together). Anyway I sent her on her way with a few books to read along with a suggestion of viewing the elegant universe dvd. My question though is there any conflicting answers of ages from dating techniques. As far as I remember, although my memory isn’t perfect I thought that the common idea was the Universe being around 11 billion years old and the earth being 4.5-6 billion years old

Those that believe the Earth is 10,000 years old are basing their belief on Scripture. They simply would rather believe the word of God than scientists. They are not going to change their mind based on the arguments of a physics student, nor should they.

I certainly knew some Young-Earthers in my youth. One of them was a preacher's kid, and he insisted also that human males have one less rib than females do. I was quite sure he was wrong, but I couldn't find anything around our house in the way of a medical book to take to him and show him. His family moved to Michigan after just a few years, and I sometimes wonder what became of them.

My question though is there any conflicting answers of ages from dating techniques. As far as I remember, although my memory isn’t perfect I thought that the common idea was the Universe being around 11 billion years old and the earth being 4.5-6 billion years old

Maybe someone else can chime in wrt the age of the Earth (or dating applied to rocks in general); IIRC the principal method used is a comparison of the relative abundance of various isotopes that are the decay products of a radioisotope (e.g. potassium 40, uranium 238), in rocks where other evidence strongly suggests no further chemical processing (e.g. weathering).

For the universe the story is considerably more complicated and, until recently, there were inconsistencies in the derived age of the universe, from different methods. Briefly, and leaving out many details that may be interesting (and important; depends on your purpose):
- stars: once a star settles down onto the Main Sequence, its fate is pretty predictable, even if it's in a binary system (detailed understanding of the evolution of binary systems is quite recent). Reversing the picture - from the observed properties of a star, work out its age - is fairly straight-forward, and yields good estimates when you have a bunch of stars which formed at the same time (a 'cluster'). The oldest cluster says that the universe is older still.
- the cosmic microwave background radiation: this is the vastly red-shifted light from the 'surface of last scattering', the time when electrons and protons combined to form neutral H atoms (it's redshifted because the universe is expanding). From the temperature of this radiation, plus the temperature at which H atoms form (in a cooling universe), plus a cosmological model that's consistent with all astronomical data, you get the age of the universe. WMAP has perhaps the best age so determined (the site is a good one; lots of fascinating stuff!)
- there are other methods too, but this post is already too long!

Until recently, there was an irritating discrepancy between the derived ages of the oldest globular clusters and the age of the universe derived from analysis of the CMBR; the former were greater than the latter. Part of the problem was with H, the Hubble constant, which is the rate of expansion of the (local) universe (it's given in weird units - km/s/Mpc - kilometres per second per megaparsec!). This parameter has a long history and has been very difficult to determine with a satisfying level of accuracy (partly for this reason astronomers - among themselves - don't talk about the distance to galaxies in terms of Mpc, rather in terms of z, the redshift). Within the last ten years or so the error bars on determinations of H have been reduced considerably. As a result, there's no conflict between the age of the universe as determined from the various dating techniques used.